We now proceed to examine the influence of directly contrasting the characteristic times of adsorption and desorption, along with the initial interface saturation through varying \(k\)  and \(Da\)  simultaneously. This concurrent variation allows us to maintain all other parameters constant. Figure REF (a) portrays a monotonic response of the cavity depth and \(\tilde{\Gamma }\)  with \(k\)  and \(Da\) , where the rapid rates of surfactant adsorption inherent to the high \(k\)  (low \(Da\) ) cases are materialised in the relatively large and comparatively constant \(\tilde{\Gamma }\)  distributions along the cavity. In line with our previous results, general reductions in local surface tension at the bubble rear, brought about by higher \(k\)  or \(\beta _{s}\)  and lower \(Bi\)  conditions, promote a faster and deeper infiltration of liquid into the bubble domain. In figure REF (b) we record the time until the first pinch-off instance at the bubble interior as a function of \(k\)  for the entire parameter space explored. A retardation of the capillary instabilities that lead to end-pinching is seen as \(k\)  is increased in the range 0 (surfactant-free) \(< k < 1\) , consistent with our previous remarks about the combined effect of \(\tilde{\sigma }\)  and Marangoni stresses on opposing drop encapsulation. This behaviour is mirrored by the \(\tilde{\tau }_{m}\)  and \(\tilde{\kappa }\)  peaks exposed in the vicinity of the nascent pinching necks for the lowest \(k\)  cases displayed in figure REF (a) (\(k = 0.1 - 1.0\) ), while the oscillations seen for \(k = 10\)  correspond to capillary waves in the liquid cavity, as reported by [1]} for long liquid ligaments.
